Solve for I
\left\{\begin{matrix}I=\frac{NPR}{100S}\text{, }&S\neq 0\\I\in \mathrm{R}\text{, }&\left(P=0\text{ or }N=0\text{ or }R=0\right)\text{ and }S=0\end{matrix}\right.
Solve for N
\left\{\begin{matrix}N=\frac{100IS}{PR}\text{, }&R\neq 0\text{ and }P\neq 0\\N\in \mathrm{R}\text{, }&\left(S=0\text{ and }P=0\right)\text{ or }\left(S=0\text{ and }R=0\right)\text{ or }\left(I=0\text{ and }P=0\right)\text{ or }\left(I=0\text{ and }R=0\right)\end{matrix}\right.
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100SI=PNR
Multiply both sides of the equation by 100.
100SI=NPR
The equation is in standard form.
\frac{100SI}{100S}=\frac{NPR}{100S}
Divide both sides by 100S.
I=\frac{NPR}{100S}
Dividing by 100S undoes the multiplication by 100S.
100SI=PNR
Multiply both sides of the equation by 100.
PNR=100SI
Swap sides so that all variable terms are on the left hand side.
PRN=100IS
The equation is in standard form.
\frac{PRN}{PR}=\frac{100IS}{PR}
Divide both sides by PR.
N=\frac{100IS}{PR}
Dividing by PR undoes the multiplication by PR.
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